The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  2  2  1  4  1  0  1  1  2  1  4  1  2
 0 12  0  4  0  0  4 12  8 12  0 12  0 12  8 12  8  8  4 12  8  8 12 12 12 12  4 12  8  8  8  8  4  4  8  4  4  8  0  8  8  0 12  8  0  0  0 12  0  4  8 12  0
 0  0 12  4  0 12  4  8  4  4  0  0  0  4  4  8  4  8 12 12  0  4  0  8  0  8  4  4  8 12  0 12  8  0  4  4 12  4 12  4  4 12  0  4  4  4  4 12  0 12  4 12  8
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  0  8  8  0  0  8  0  0  8  8  8  0  0  0  0  0  8  0  8  0  0  8  8  0  8  0
 0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  0  0  0  0  8  8  0  8  0  0  8  8  0  8  0  0  0  0  8  0
 0  0  0  0  0  8  0  0  8  0  8  8  0  8  0  0  8  8  8  8  8  0  8  0  8  8  0  8  8  0  0  8  8  0  8  8  8  8  0  0  0  0  0  0  0  8  8  0  0  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  0  8  0  8  8  0  8  8  8  8  0  0  0  8  8  0  8  8  8  8  0  0  8  0  8  8  8  0  0  8  8  0  8  8  8  8

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+88x^46+199x^48+232x^50+384x^51+785x^52+768x^53+806x^54+384x^55+197x^56+115x^58+78x^60+34x^62+18x^64+4x^66+1x^68+1x^74+1x^88

The gray image is a code over GF(2) with n=424, k=12 and d=184.
This code was found by Heurico 1.16 in 0.517 seconds.